|
%I #20 Sep 10 2016 10:21:05
%S 1,3,13,67,378,2244,13737,85767,542685,3466515,22298796,144210388,
%T 936575968
%N Number of 321-avoiding extensions of comb K_{s,2}^{alpha}.
%C No formula is presently known.
%C From _Colin Defant_, Aug 16 2016: (Start)
%C For each subset W={w_1,w_2,...,w_k} of {n+1,n+2,...,2n} satisfying w_1<w_2<...<w_k, let H(W) be the number of sequences of integers i_1,i_2,...,i_k such that i_1<i_2<...<i_k and w_j-n+j<=i_j<=w_j-1 for all j. We have a(n)=Sum(H(W)), where the sum ranges over all subsets W of {n+1,n+2,...,2n}.
%C 3 + sqrt(8) <= lim_(n->oo)a(n)^(1/n) <= 27/4. (End)
%H C. Defant, <a href="http://arxiv.org/abs/1608.03951">Some Poset Pattern-Avoidance Problems Posed by Yakoubov</a>, arXiv:1608.03951 [math.CO], 2016.
%H S. Yakoubov, <a href="http://arxiv.org/abs/1310.2979">Pattern Avoidance in Extensions of Comb-Like Posets</a>, arXiv preprint arXiv:1310.2979 [math.CO], 2013.
%K nonn,more
%O 1,2
%A _N. J. A. Sloane_, Dec 28 2013
%E a(7)-a(13) from _Colin Defant_, Aug 16 2016
|
